Tank Volume Calculator (cylinder, rectangular & capsule, partly filled)

Understanding the tank volume calculator — concept and principle

This calculator finds the total capacity of a tank and how much liquid is in it at a measured depth. It handles vertical and horizontal cylinders, rectangular tanks and capsule tanks with rounded ends. Use it for heating-oil tanks, water storage, rain tanks and fuel tanks when you can only dip a stick.

The liquid fills a circular segment; below half depth it holds less than the depth suggests.

How it is calculated

Cylinder capacity = π r² L; rectangular tank = width × length × height.
Capsule capacity = π r² (L − 2r) + 4⁄3 π r³ (a cylinder plus a hemisphere at each end, L measured end to end).
Vertical cylinder filled to depth h: π r² h.
Horizontal cylinder filled to depth h: L × [r² arccos((r − h) ÷ r) − (r − h) √(2rh − h²)].
Horizontal capsule: the straight part as above plus a spherical cap π h² (3r − h) ÷ 3 for the two ends together.

Sizes in cm give cm³; ÷ 1,000 gives litres. 1 US gallon = 3.785411784 L.

The principle

In an upright tank the cross-section is the same at every height, so volume rises in step with depth. A horizontal cylinder is different: its width changes with height, so the first and last few centimetres hold little and the middle holds the most. The bracket in the formula is the area of a circular segment, the part of a circle below a chord at depth h; multiplying by the length gives the liquid volume. Rounded ends add spherical caps: two half-spheres filled to the same depth together form one cap of a sphere.

Worked example

Default inputs: horizontal cylinder, diameter 120 cm, length 250 cm, liquid depth 45 cm.

Radius r = 60 cm; capacity = π × 60² × 250 = 2,827,433 cm³ = 2,827.43 L (2.827 m³).
Segment area = 60² × arccos(15 ÷ 60) − 15 × √(2 × 60 × 45 − 45²) = 3,600 × 1.3181 − 15 × 58.09 = 3,873.8 cm².
Liquid = 3,873.8 × 250 ÷ 1,000 = 968.45 L, which is 255.84 US gallons.
Fill level = 968.45 ÷ 2,827.43 = 34.3 %; space left = 1,858.98 L.

Each point is the calculator re-run with only “Liquid depth, measured from the bottom (cm)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Liquid depth, measured from the bottom (cm)	Liquid in the tank (litres)
11.2	133.84
22.5	367
33.8	652.11
45	968.45
56.2	1,301.29
67.5	1,638.13
90	2,274.67

How to read the result

Notice that the tank is 37.5 % full by depth (45 of 120 cm) but only 34.3 % full by volume. Below half depth a horizontal tank always holds a smaller share than the depth suggests, and above half depth a larger share. Use the space left when ordering a delivery, and leave the headroom that the tank maker or supplier asks for.

Common mistakes

Using outside dimensions instead of inside dimensions.
Treating a horizontal tank as if volume were proportional to depth.
Measuring a capsule's length without the rounded ends.
Applying hemispherical ends to tanks with flatter dished ends.

Keep in mind: Wall thickness, fittings, sludge and dished ends change the true volume. For fuel or chemical tanks, use the maker's calibration chart where one exists.

Frequently asked questions

How do I measure the liquid depth?

Lower a clean dipstick straight down at the centre to the bottom and read the wet mark.

How many litres is a cubic metre?

Exactly 1,000 litres.

Why does a half-depth horizontal tank hold half its volume?

At exactly half depth the circle is cut through its centre, so the segment is exactly half the circle.

Sources: D. Zwillinger (ed.), CRC Standard Mathematical Tables and Formulas, 33rd ed. (2018), Geometry · NIST Special Publication 811 (1 US gallon = 3.785411784 L)

Checked 9 Nov 2026. Volumes of the cylinder, sphere and spherical cap and the area of a circular segment: D. Zwillinger (ed.), CRC Standard Mathematical Tables and Formulas, 33rd ed. (2018), §4 (Geometry); 1 US gallon = 3.785411784 L (NIST SP 811).

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